Filter IIR (Butterworth) and ICA

for Identifying Silent Chain’s Sound Characteristics

Rika Novita Wardhani, David Putra Yohast, Iqro Sari Tilawah

Politeknik Negeri Jakarta, Jurusan Teknik Elektro, Prodi Instrumentasi dan Kontrol Industri,

Jl Prof. DR. GA Siwabessy, Kampus Baru UI Depok 16425

Keywords: Butterworth, IIR, Filter, ICA, Independent Component Analysis, Silent Chain, Sound, Audio, Characteristics,

Separation, Frequency, Hz.

Abstract: X Company as a silent chain manufacturer has a problem identifying the silent chain’s sound characteristics

for comparison among other products. Sound characteristics of the silent chain consist of amplitude,

frequency, and sound pressure level (SPL). To attain sound characteristics, a filter that can separate the silent

chain’s audio among other components is needed. Two options that sprout are Butterworth Filter and also

ICA. The design of the Butterworth filter is based on identifying the pulse transfer function H(z) that satisfies

the requirements of the filter specification. ICA uses mathematical and statistical approaches to decompose

components in the observed data set. Singular Value Decomposition (SVD) model used in ICA. In application,

sound sources attained from test rig which is consists of a silent chain set (gear, silent chain, and a DC motor).

The filter program will be made in Matlab software with a time-domain plot and spectrogram as the outputs.

ICA and Butterworth filter can separate silent chain audio. Silent chain’s frequencies were ranged from 7000-

14000 Hz, and the motor’s frequencies are ranged from 0-1000 Hz. As a comparison, the Butterworth filter

can work better than ICA because it can minimize noise frequency cleaner and the silent chain's frequency

more visible.

1 INTRODUCTION

PT. X is a manufacturing company that produces

Silent chains. In its development, the chain is better

than the roller chain. The main advantage of the silent

chain is that the sound is quiet and able to operate at

a higher speed than the roller chain, which is currently

widely used in the industrial as a mechanical power

transfer. But, there is no data regarding the

characteristics of Silent chain sound, where the data

can be used as one of the ingredients for the

comparison of competitor products. In addition, the

determination of the characteristics of the silent chain

is inseparable from the basic reference to be used.

Determination of the sound characteristics

required for the silent chain, such as sound,

frequency, amplitude and sound pressure level

(GOYAL, 2018). To solve the problems, the authors

made a test rig design to simulate the sound of a silent

chain. But, there is a challenge in determining

characteristics of sound (Maulana & Andono, 2016),

which is the sound of a silent chain that has mixed up

with other components. So, filter the sound is needed

to get the actual silent chain’s sound characteristics

(Hansen, n.d.).

A digital filter IIR (Infinite Impulse Response)

with a Butterworth response and ICA (Independent

Component Analysis) filter used to analyze the

sound. And the A-weighted filter (A-weighted filter)

is used to provide a response that has a basic

international standard (SI). The filter is used to

improve signal quality, such as removing or reducing

noise, to retrieve information signals or to separate

two or more signals that were previously combined

(Lie, 2017).

A MATLAB program is used to process the sound

data with the output in the form of sound

characteristics of the silent chain (Mathworks, 2008).

Filtering with a digital filter IIR using the Butterworth

response is best used for audio signals because it has

a flat response in the passband and stopband (no

ripples). So in its use, this filter is able to produce a

better output signal. An ICA filter will be designed to

separate the silent chain sound from the motor.

Singular Value Decomposition (SVD) method is used

as ICA mathematical modeling. Namely determining

114

Wardhani, R., Yohast, D. and Tilawah, I.

Filter IIR (Butterworth) and ICA for Identifying Silent Chain’s Sound Characteristics.

DOI: 10.5220/0009906800002905

In Proceedings of the 8th Annual Southeast Asian International Seminar (ASAIS 2019), pages 114-119

ISBN: 978-989-758-468-8

the rotation matrix, stretching matrix, and rotation to

minimize the gaussian properties. And the application

of A-weighting filter in determining the

characteristics of the silent chain sound is inseparable

from the sensitivity of the human ear, therefore the

output signal from the A-weighting filter has a

standard that is in accordance with the international

standard.

2 SOUND CHARACTERISTICS

Sound basically a wave. There are two types of wave

we commonly know. There are trasnversal, and the

other one is longitudinal. Sound is one of longitudinal

waves. As a longitudinal waves, there are

compressions and rarefactions. Compression is area

where you can find dense waves in one time. And

Rarefaction is area where you can find tenuous waves

in one time. The best three items to describe

soundwave are frequency, amplitude, and time-

period.

- Frequency : The best thing to describe

frequency is number of waves per time. Or

commonly, we called as number of waves per second.

- Amplitude : When you draw waves in 2D,

you can see normal line, and commonly there are

some point that have peak state (in y line). That peak

is called amplitude, or we can say the maximum

displacement from its normal line. This phenomenon

caused by particles of the medium get displaced

temporarily from their original undisturbed positions.

The International unit of amplitude is metre (m) but

sometimes it is also measured in centimetres.

- Time-Period : The best definition to time-

period is time required by a wave to complete it’s one

cycle. In 2D explanation, you can describe it by

‘mountain’ and ‘valley’. Or we called as full

vibration. Symbol of time-period is T, and the unit is

second (s). (GOYAL, 2018).

3 IIR (INFINITE IMPULSE

RESPONSE) FILTER

Infinite Implus Response or IIR is filter in that the

output is computed using current and previous input,

in addition also the current and previous output.

Because of that, this filter is called recursive filter

because the output is not straightforward used, but

calculated again and again. This filter uses Transfer

Function (Hz) that met the requirement of the filter

specifications. This method encourage the user to

make analogue model, and transform into pulse

transfer. Alternately, you can use digital design.

(Tutorials, 2018).

Basically transfer function of IIR filter which has n

orde is :







Bz

Az





b





…b





1a





⋯b





(1)

Where :

H(z) = transfer function of IIR filter

a1, a2 = feedback coefficient IIR filter

b1, b2 = feed forward coefficient IIR filter

The frequency response of the Butterworth Filter

approximation function is also often referred to as

“maximally flat” or when you see in graphs, there are

no some kind of noise, or we called it a ripple. So in

context of sound, when you want a certain frequency

band as your output, then in the result you won’t hear

some sound from frequency outside your chosen

band. (Brown, 2014).

Figure 1: Frequency Response of Butterworth

In this research, author uses the bilinear transform

(transformation from continuous-time systems to

discrete-time systems (in the Z-domain)). This

method has two following characters:

- If H (s) of the laplace transformation is a

causal and stable LTI system, then H (z) will be

causal and stable.

- The characteristics of H (s) are as initial

characteristics of the characteristics of H (z) meaning

that in this method the H (s) is needed (Komal Singla,

2014).

4 ICA (INDEPENDENT

COMPONENT ANALYSIS)

FILTER

Listeners get lots of signal sources every day and

every time. Whether it comes from friction (sound

waves), or electromagnetic signals that we can not

Filter IIR (Butterworth) and ICA for Identifying Silent Chain’s Sound Characteristics

115

catch directly, but we feel (for example through

television or radio) (Aapo Hyvärinen, 2000).

Listeners deal with these signals every day. However,

due to external situations, it is not possible to get

signals purely, but signals are mixed (linearly mixed)

that we can observe. Because humans get the signal

already in mixed form, then this signal is often also

called naturally mixed / linearly mixed. Listeners

want the original signal for analysis and other

purposes. This is the problem of Blind Source

Separation, which is to get the original signal from a

signal that is naturally mixed / linearly mixed and by

observation, indeed only that signal is obtained

(Atmaja, Aisyah, & Arifianto, 2010).

To begin the process with ICA, it must start with

a simple abstract, namely with the Cocktail Party

Problem approach as explained in the previous

discussion (Filho, 2012). People who want to use ICA

must understand ICA abstractly why ICA should be

used. Therefore, with the Cocktail Party Problem

approach, people will easily understand that ICA will

output one signal source from naturally mixed /

linearly mixed signals. Of course, this output does not

always produce good quality or perfect output

because the method is still being developed and will

continue to develop (Kutz, Independent Component

Analysis 1, 2018). However, at least with the ICA

method, the components of the ICA process will be

seen and can be seen as its characteristics even though

it is not perfect (Shangmeng He, 2017).

The simple formulation of the object observed

with existing components can be written as follows:







(2)

Where x is the sound that is heard (natural mix),

A is the mixing matrix (mixing matrix), and s is a

component (sound source) (Kutz, Independent

Component Analysis 2, 2018).

The Singular Value Decomposition approach will

assume that A is a complex matrix and can be derived

into:





∑



∗

(3)

Therefore, the previous equation can be changed

to:











∑



∗







(4)

Because you want to find the components, then

from the formulation above, you must make an

inversion, that is:







∗







(5)

Where



∗





















(6)

∑































(7)





cos



sin



sin



cos





(8)

(Kutz, Independent Component Analysis 3, 2018)

5 RESEARCH METHODOLOGY

5.1 Sound Identification

The main approach to this methodology is

quantitative method, because we’ll play with numbers

and data driven. To attain the data, need to identify

the sound. Reading data sheets and also study

literature about silent chain needed in this step.

5.2 Sound Sampling

The next step is doing some recording to get the sound

sampling. In this step, collaborating with mechanical

team will be an advantage. An accoustic room is

needed to reducing noise, All sound in different

environtment were sampled. After that, pull a

conclusion to best describe the silent chain characters,

such as frequency, amplitude, and period.

5.3 Filter Design

After we get some datas regarding silent chain sound,

then it’s time to design the filter. For Butterworth

(IIR) filter, a table for frequency start and cut-off is

needed, and some calculations to gain the

amplification of Butterworth filter to get the best

results. For ICA Filter, designing will be tricky, need

choose the best method to define the random matrix.

For this case, the best method is Singular Value

Decomposition because it can directly process the

sound amplitude into ICA process.

5.4 Transform and Load

The next step is we transform the record data into a

mathematical matrices and process it into matlab. 1

file will be processed in ICA filter, and another copy

will be processed in Butterwoth filter. The data will

transformed (by coding in ICA filter design, or by

coding in Butterworth filter design). Finally, load it

using graphs and add some insightful information.

6 RESULTS

From the silent chain recordings, amplitude datas can

be visualized as a time-domain graph and frequency-

ASAIS 2019 - Annual Southeast Asian International Seminar

116

domain graph. For a convenient use, a spectrogram

can be used to analyze frequency spektrum for each

time-domain.

Figure 2: (upper) a time-domain plot from recording

data, (center) a frequency-domain plot from recording

data, (lower) a spektrogram of frequencies spektrum

in time-domain.

That is data from recording section that had been

done by microphone + software.

6.1 Butterworth Design and Result

Make a design for identify the filter specification

from data attained from figure 2 :

Table 1: Filter Specification

10 Khz

12 Khz

13 Khz

15 Khz

Fs 44100

(attenuation) 1 dB

(attenuation) -25dB

From the specification, there are two pass band

frequencies, fp1 and fp2, and two stop band

frequencies, fs1 and fs2. So it is known that the type

of filter design is between the band pass filter and the

band stop filter. From the value of fp1 and fp2 where

the value of fp1 is greater than fs1, it can be concluded

that the filter used is a type of band pass filter.

For filtering, we need an orde of the filter. But

from the specification, we have to determine the

frecuency cut off. So, we got the orde of the filter is :













































.



,







.









.











.







0.258925412

315.2278



2

14.60483064





3.085449789

2.32899305

1.324799912

2

(9)

Then, do the transfer function H(z) of LPF

(10)

Then, do the Y(z)









1











1







0.136305912









0.004424391







Filter IIR (Butterworth) and ICA for Identifying Silent Chain’s Sound Characteristics

117

0.004383061











0.003451052











0.054610233











0.032459278











0.004765547

(11)

Figure 3: Signal After Filter

From figure 3, the frequency spectrum was more

concentrated at one ranged frequency.

6.2 ICA Design and Result

From these measurement data, a filter mathematical

model can be made. ICA Filter Mathematical Model

(12)

From ICA Filter, the result is two data that must

be analyzed, which one that can reflects which

component.

Figure 4: Two Signals After Filter

From figure 4, most likely better signal is the

upper one. Because it can focus to silent chain’s audio

frequencies. But on that graph, we can still see the

lower frequency still exist (not completely filtered).

7 CONCLUSIONS

As a final comparison, signal after filter give more

insight if we see the Butterworth one. But you must

know that to make / design Butterworth Filter, it’s not

easy, and you must calculate it meticulously.

Because, different with ICA which doesn’t compel

the researcher to have some prior knowledge,

Butterworth filter compel the researcher to have

knowledge about frequencies, attenuation, and etc.

ICA filter as a new research method to sound

separation not give a quite good filtered signal. But

the result was quite impressive. Because after design

the mathematical model, researcher can just study

from one certain component to find out which one the

silent chain’s frequency, and which one that don’t.

As a filter, Butterworth is dependable and reliable.

Its method and result is excellent and can make noise

frequencies ‘disappear’ completely. But, researcher

must know in the first time, what the silent chain’s

frequency range is, and must know to what extent the

attenuation is permitted.

The final characteristics of silent chain is from

7000 Hz to 14000 Hz. And the motor is 0 Hz – 1000

Hz. Both filter succeed to passing the 7000 Hz –

14000 Hz frequencies.

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Neural Networks, 20.

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Menggunakan Independent Component Analysis (ICA)

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